What is the difference between:
The objective of the project is to develop a framework
Versus:
The objective of the project is developing a framework
Is any of them incorrect?
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An objective is an aim, or purpose, so it is correct to say "the objective is to develop a framework" ('develop' being the infinitive form of the verb).
The objective of the project is to develop a framework
Your alternate example with "...is developing" is not strictly correct. Remember that you are talking about the objective of the project, not the project itself. The objective will not be developing anything. You might say that "the project team is developing a framework" because that is who is actually carrying out the action. However, it seems some people do use it.
Another alternative way to express this that is grammatically acceptable and uses the present participle is to use it with the definite article:
The objective of the project is the developing of a framework.
Quotations: